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We consider biperversities and prove that there is a K\\\"unneth theorem relating $I^{\\bar p,\\bar q}H_*(X\\times Y)$ to $I^{\\bar p}H_*(X)$ and $I^{\\bar q}H_*(Y)$ for all choices of $\\bar p$ and $\\bar q$. Furthermore, we prove that the Kunneth theorem still holds when the biperversity $p,q$ is \"loosened\" a little, and using this we recover the Kunneth "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0808.1750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-08-12T23:07:04Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f3eef1aea13c528d373973264b0f2bf340871e22a9860c2b6aae4e87ec4be145","abstract_canon_sha256":"464f8b49792dd549862d94d8381629cf439eff63cf5d706e2ac97c6c7efce38d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:28.842370Z","signature_b64":"Rck+TcNh74Jt6dIxu20B+KZ7MBR+0/xuODUPMIKqxfDHb92sRz9lmD89viTgfphyw7+FLrMePQ0jO52IA9BRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5062097b75e4c0fe7f8a55ff39301db46adacd5c501b0b6189907e6e5583a96a","last_reissued_at":"2026-05-18T04:25:28.841869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:28.841869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection homology Kunneth theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Greg Friedman","submitted_at":"2008-08-12T23:07:04Z","abstract_excerpt":"Cohen, Goresky and Ji showed that there is a Kunneth theorem relating the intersection homology groups $I^{\\bar p}H_*(X\\times Y)$ to $I^{\\bar p}H_*(X)$ and $I^{\\bar p}H_*(Y)$, provided that the perversity $\\bar p$ satisfies rather strict conditions. We consider biperversities and prove that there is a K\\\"unneth theorem relating $I^{\\bar p,\\bar q}H_*(X\\times Y)$ to $I^{\\bar p}H_*(X)$ and $I^{\\bar q}H_*(Y)$ for all choices of $\\bar p$ and $\\bar q$. Furthermore, we prove that the Kunneth theorem still holds when the biperversity $p,q$ is \"loosened\" a little, and using this we recover the Kunneth "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1750","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0808.1750","created_at":"2026-05-18T04:25:28.841938+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.1750v1","created_at":"2026-05-18T04:25:28.841938+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1750","created_at":"2026-05-18T04:25:28.841938+00:00"},{"alias_kind":"pith_short_12","alias_value":"KBRAS63V4TAP","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"KBRAS63V4TAP474K","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"KBRAS63V","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR","json":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR.json","graph_json":"https://pith.science/api/pith-number/KBRAS63V4TAP474KKX7TSMA5WR/graph.json","events_json":"https://pith.science/api/pith-number/KBRAS63V4TAP474KKX7TSMA5WR/events.json","paper":"https://pith.science/paper/KBRAS63V"},"agent_actions":{"view_html":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR","download_json":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR.json","view_paper":"https://pith.science/paper/KBRAS63V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.1750&json=true","fetch_graph":"https://pith.science/api/pith-number/KBRAS63V4TAP474KKX7TSMA5WR/graph.json","fetch_events":"https://pith.science/api/pith-number/KBRAS63V4TAP474KKX7TSMA5WR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR/action/storage_attestation","attest_author":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR/action/author_attestation","sign_citation":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR/action/citation_signature","submit_replication":"https://pith.science/pith/KBRAS63V4TAP474KKX7TSMA5WR/action/replication_record"}},"created_at":"2026-05-18T04:25:28.841938+00:00","updated_at":"2026-05-18T04:25:28.841938+00:00"}